A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**Fairview High School Anime Club Participation Analysis**
Fairview High School offers an anime (Japanese animation) club that all students can join. The following relative frequency table illustrates the proportion of students at the high school who either take Japanese, are part of the anime club, or both.
| | Take Japanese | Do not take Japanese | Total |
|---------------------|---------------|----------------------|-------|
| **In anime club** | 0.15 | 0.01 | 0.16 |
| **Not in anime club** | 0.05 | 0.79 | 0.84 |
| **Total** | 0.20 | 0.80 | 1.0 |
**Explanation**
- **Take Japanese and In anime club**: 15% of students take Japanese and are in the anime club.
- **Take Japanese and Not in anime club**: 5% of students take Japanese but are not in the anime club.
- **Do not take Japanese and In anime club**: 1% of students do not take Japanese but are in the anime club.
- **Do not take Japanese and Not in anime club**: 79% of students do not take Japanese nor are they in the anime club.
**Total Proportions**
- 20% of students take Japanese courses.
- 80% of students do not take Japanese courses.
- 16% of students are in the anime club.
- 84% of students are not in the anime club.
**Probability Question**
Given that a student takes Japanese, what is the likelihood that they are in the anime club?
To find this probability, use the following formula:
\[ P(\text{In anime club} \mid \text{Take Japanese}) = \frac{P(\text{In anime club and Take Japanese})}{P(\text{Take Japanese})} \]
\[ = \frac{0.15}{0.20} = 0.75 \]
Thus, the likelihood that a student who takes Japanese is also in the anime club is 75%.](https://content.bartleby.com/qna-images/question/e5e18cbe-2086-4486-bcaa-95b482346f76/6bb7dccb-97bc-4d8a-9623-64afad15077a/0aww0xd_processed.jpeg)
Transcribed Image Text:**Fairview High School Anime Club Participation Analysis**
Fairview High School offers an anime (Japanese animation) club that all students can join. The following relative frequency table illustrates the proportion of students at the high school who either take Japanese, are part of the anime club, or both.
| | Take Japanese | Do not take Japanese | Total |
|---------------------|---------------|----------------------|-------|
| **In anime club** | 0.15 | 0.01 | 0.16 |
| **Not in anime club** | 0.05 | 0.79 | 0.84 |
| **Total** | 0.20 | 0.80 | 1.0 |
**Explanation**
- **Take Japanese and In anime club**: 15% of students take Japanese and are in the anime club.
- **Take Japanese and Not in anime club**: 5% of students take Japanese but are not in the anime club.
- **Do not take Japanese and In anime club**: 1% of students do not take Japanese but are in the anime club.
- **Do not take Japanese and Not in anime club**: 79% of students do not take Japanese nor are they in the anime club.
**Total Proportions**
- 20% of students take Japanese courses.
- 80% of students do not take Japanese courses.
- 16% of students are in the anime club.
- 84% of students are not in the anime club.
**Probability Question**
Given that a student takes Japanese, what is the likelihood that they are in the anime club?
To find this probability, use the following formula:
\[ P(\text{In anime club} \mid \text{Take Japanese}) = \frac{P(\text{In anime club and Take Japanese})}{P(\text{Take Japanese})} \]
\[ = \frac{0.15}{0.20} = 0.75 \]
Thus, the likelihood that a student who takes Japanese is also in the anime club is 75%.
Transcribed Image Text:**Question:**
Given that a student takes Japanese, what is the likelihood that he or she is in the anime club?
**Answer Choices:**
- **A.** 20%
- **B.** 75%
- **C.** About 94%
- **D.** 15%
*Note: There are no graphs or diagrams to be explained in this image.*
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